But the partial derivatives of n are going to get ugly and I still would not be finished. I need the eigenvalues of:

$\displaystyle a^{\alpha \gamma}b_{\gamma \beta}$

Jun 30th 2009, 03:16 AM

Rebesques

It's going to be lengthy anyhow, but here's a slight improvement:
Compute the Gaussian and mean curvatures $\displaystyle K$ and $\displaystyle H$ in terms of the coefficients in the first and second fundamental forms, and remember that
the principal curvatures satisfy the equation $\displaystyle x^2-2Hx+K=0$.